If the sum of the distances of a point from the origin and the line $x = 2$ is $4$,then its locus is

$A$ variable circle is drawn passing through the origin $O$. It intersects the $X$ and $Y$ axes at points $A$ and $B$ respectively,such that $OA + 2OB = K$ (a non-zero constant). The circle always passes through a fixed point $P$ other than the origin. The point $P$ lies on -

Let the locus of the point of intersection of the perpendicular tangents drawn to the circle $x^2+y^2+6x-4y-12=0$ be the circle $S$. Then the equation of the tangent drawn to $S$ which is perpendicular to the line $6x-4y+k=0$ is

The locus of the center of a circle which touches the circle $x^{2} + y^{2} - 6x - 6y + 14 = 0$ externally and also touches the $y$-axis is:

The locus of a point which moves such that the sum of the squares of its distances from the three vertices of a triangle is constant,is a circle whose centre is at the

Let $C$ be the centre and $A$ be one end of a diameter of the circle $x^2+y^2-2x-4y-20=0$. If $P$ is a point such that $A$ divides $CP$ in the ratio $2:3$,then the locus of $P$ is